DS question: don't agree with the explanations, plz advise

[54siwei]

Question: If pq ><0 ( not equal to 0), is p^2q>p^2q?

(1) qp<0;
(2) P<0;

The answer given is C, but I don't agree because of the following reasons:

If Premises (1)&(2) don't contradict each other, it means there can only be one possible solution: p<0 and q>0;

Because p^2q>p^2q can be simplified to Pq(p-q)>0, (1) is sufficient because pq<0, p-q<0; (2) is sufficient becuase p<0, q>0, p-q<0;

So I think the answer should be D: each is sufficient.

Please
Please explain if I was wrong and why? Thank you!

This question is from Manhattan Question Bank: Algebra [equations, inequality and VICs].

[jlucero]

First, your question was copied incorrectly. Here's the real one:

If pq ≠ 0, is (p^2)q > p(q^2)?

(1) pq < 0

(2) p < 0

Second, you are falling for one of the most classic DS traps. Yes, with both pieces of information you are able to say that p is negative and q is positive. But given just statement 2, you only know that p is negative. In the original statement I would know:

(p^2)q > p(q^2) ?
(pos)q > (neg)(pos)

or

pq(p-q) > 0 ?
(neg)(q)(neg - q) > 0

If q is positive, this is true. But if q is a negative number, then it depends on whether q is more negative than p. Therefore, we don't have sufficient information to answer the question. Same thing for the first statement. Only with both statements together do I have sufficient information.